A Heuristic for 4-Colouring a Planar Graph

A technique is described that constructs a 4-colouring of a planar triangulation in quadratic time. The method is based on iterating Kempe’s technique. The heuristic gives rise to an interesting family of graphs which cause the algorithm to cycle. The structure of these graphs is described. A modified algorithm that appears always to work is presented. These techniques may lead to a proof of the 4-Colour Theorem which does not require a computer to construct and colour irreducible configurations.